A double-ridge waveguide is designed for efficient and robust second-harmonic generation (SHG) using the thin-film lithium-niobate-on-insulator (LNOI) platform. Perfect phase matching (PhM) is achieved between the fundamental waveguide mode at 1,550 nm and a higher-order mode at the second harmonic. The fabrication tolerances of the PhM condition are simulated using a finite-difference method mode solver, and conversion efficiencies as high as 3.92 W−1 are obtained for a 1-cm long waveguide. This design allows access to the largest element of the second-order nonlinear susceptibility tensor, and represents a scalable alternative to waveguides based on periodically-poled lithium niobate (PPLN). The design has the potential for generating pairs of entangled photons in the infrared C-band by spontaneous parametric down-conversion (SPDC).